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Transactions of the American Mathematical Society

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Operators with $ C\sp{\ast} $-algebra generated by a unilateral shift


Authors: John B. Conway and Paul McGuire
Journal: Trans. Amer. Math. Soc. 284 (1984), 153-161
MSC: Primary 47B20; Secondary 47C15
DOI: https://doi.org/10.1090/S0002-9947-1984-0742417-7
MathSciNet review: 742417
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Abstract: If $ T$ is an operator on a Hilbert space $ \mathcal{H}$, this paper gives necessary and sufficient conditions on $ T$ such that $ {C^{\ast} }(T)$, the $ {C^{\ast} }$-algebra generated by $ T$, is generated by a unilateral shift of some multiplicity. This result is then specialized to the cases in which $ T$ is a hyponormal or subnormal operator. In particular, it is shown how to prove a recent conjecture of C. R. Putnam as a consequence of our result.


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DOI: https://doi.org/10.1090/S0002-9947-1984-0742417-7
Keywords: Hyponormal operator, $ {C^{\ast} }$-algebra, unilateral shift, subnormal operators
Article copyright: © Copyright 1984 American Mathematical Society